Flying with babies

So my husband and I will be flying to our home state two months after the baby is born to visit family (since I get 3 months off might as well use this time to visit family ) . I was wondering how everyone flies with there kids. I read that it’s safer to have your baby in the car seat (which you have to pay the extra seat for ) but I was recently reading that you shouldn’t have your baby in a car seat for more than an hour and this would be a total of a 9-12 hour flight .

So I guess what I’m asking is would you fly with your baby in a car seat or not ? What did you find that worked out for you ?